A mathematical model for simulating the biogeochemical processes in a freshwater lake

The most significant chemical elements in a lake ecosystem are phosphorus and nitrogen because one of them is the limiting factor of primary production rate. The phosphorus content level in a freshwater lake is of substantive importance in prediction of phytoplankton blooms. In that regard, the problem of the development of integrative models aimed at numerical simulation of the biochemical processes of phosphorus and nitrogen limitation in am aquatic ecosystem is topical for the contemporary stage of the development of mathematical methods in problems of limnology.
In this paper, a mathematical model for studying the environmental status of a freshwater lake is proposed. The model includes ten prognostic variables: nitrate, phosphate, ammonium, chlorophyll a, phytoplankton, zooplankton, small nitrate detritus, large nitrate detritus, small phosphate detritus, and large phosphate detritus. Calculations performed based on the model developed for Barguzin Bay of Lake Baikal showed that during last ten days of August:

• increased chlorophyll a content in the pelagic zone of the lake is localized at depths of 1030 m;
• zooplankton is concentrated in the upper 25 m layer, and its biomass grows faster in the open water area;
• the decrease in nutrients is registered in the zones with high phyto- and zooplankton populations.

The results obtained are in qualitative agreement with data from monitoring studies of the chemical composition of water in Lake Baikal in summer.